Class 8 Maths Exercise 3.2 Easy Solutions NCERT

Class 8 Maths Exercise 3.2 Easy Solutions NCERT focuses on understanding the properties of quadrilaterals. In this exercise, students learn to identify and work with different types of quadrilaterals, such as parallelograms, rectangles, and squares, by applying key concepts. The easy, step-by-step solutions provided are based on the NCERT textbook, offering clear and simple explanations to help you grasp the concepts better. With these solutions, you’ll be able to solve problems involving angles, sides, and properties of various quadrilaterals with confidence.

Class 8 Maths Exercise 3.2 Easy Solutions NCERT

Ex 3.2 Class 8 Maths Question 1.
Find x in the following figures.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q1
Solution:
(a) We know that the sum of all the exterior angles of a polygon = 360°
125° + 125° + x = 360°
⇒ 250° + x = 360°

x = 360° – 250° = 110°

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Hence x = 110°
(b) Here ∠y = 180° – 90° = 90°

Class 8 Maths Exercise 3.2 Easy Solutions NCERT

and ∠z = 90° (given)
x + y + 60° + z + 70° = 360° [∵ Sum of all the exterior angles of a polygon = 360°]
⇒ x + 90° + 60° + 90° + 70° = 360°
⇒ x + 310° = 360°
⇒ x = 360° – 310° = 50°
Hence x = 50°

Ex 3.2 Class 8 Maths Question 2.
Find the measure of each exterior angle of a regular polygon of
(i) 9 sides
(ii) 15 sides
Solution:
(i) We know the sum of all the exterior angles of polygon = 360°
Measure of each angle of 9 sided regular polygon = 3609 = 40°
(ii) Sum of all the exterior angles of a polygon = 360°
Measure of each angle of 15 sided regular polygon = 36015 = 24°

Ex 3.2 Class 8 Maths Question 3.
How many sides does a regular polygon have if the measure of an exterior angle is 24°?
Solution:
Sum of all exterior angles of a regular polygon = 360°
Number of sides
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q3
Hence, the number of sides = 15

Ex 3.2 Class 8 Maths Question 4.
How many sides does a regular polygon have if each of its interior angles is 165°?
Solution:
Let re be the number of sides of a regular polygon.
Sum of all interior angles = (n – 2) × 180°
and, measure of its each angle
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q4
Hence, the number of sides = 24

Ex 3.2 Class 8 Maths Question 5.
(a) Is it possible to have a regular polygon with measure of each exterior angle a is 22°?

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q5

not a whole number.
Since number of sides cannot be in fractions.
It is not possible for a regular polygon to have its interior angle = 22°.

Ex 3.2 Class 8 Maths Question 6.
(a) What is the minimum interior angle possible for a regular polygon? Why?
(b) What is the maximum exterior angle possible for a regular polygon?
Solution:
(a) Sum of all interior angles of a regular polygon of side n = (n – 2) × 180°
The measure of each interior angle
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q6
The minimum measure the angle of an equilateral triangle (n = 3) = 60°.
(b) From part (a) we can conclude that the maximum exterior angle of a regular polygon = 180° – 60° = 120°.